The comparative studies, available in literature and addressed to the modelling of unreinforced (URM) buildings, document a large scattering of achievable results, especially when used to finalize the seismic assessment through nonlinear analyses. This is mostly due to the too many possible choices in defining the numerical model and in interpreting the results. As evidence of this, the challenging topic is highlighted by both: research works specifically addressed to test different modelling strategies (e.g. Salonikios et al. 2003; Giamundo et al. 2014; Betti et al. 2014), considering also commercial software packages (e.g. Marques and Lourenco 2011; 2014; Calderoni et al. 2015; De Falco et al. 2017; Siano et al. 2018; Aşıkoğlu et al. 2020); or blind predictions involving a large number of research teams called to predict the seismic response of the same benchmark prototype (e.g. in Mendes et al. 2017; Esposito et al. 2019; Bartoli et al. 2017; Parisse et al. 2021).
While other literature works already provided an in-depth state-of-the-art of the different options involved in the equivalent frame modelling process (Quagliarini et al. 2017) or a discussion on the repercussions of some of them in the seismic assessment (Rota et al. 2014; Bracchi et al. 2015; Cattari et al. 2021a; Manzini et al. 2021), in this paper the main objective is to quantify the dispersion of achievable results when using different SWs: firstly, by setting the models with shared and consistent modelling assumptions (Sect. 3); secondly, by investigating the sensitivity of the seismic response to some common epistemic and modelling uncertainties (Sect. 4). In particular, in Sect. 3 the comparison is made in terms of total masses, dynamic parameters (periods and modal shapes obtained from the execution of a modal analysis) and results from nonlinear static analyses (e.g. pushover curve, parameters of the equivalent bilinear curve and damage occurred in structural elements). In Sect. 4, the effect of alternative equivalent frame idealization criteria adopted for masonry walls, the role of the out-of-plane contribution of piers and different assumptions for the effectiveness of wall-to-wall connections are investigated by analyzing the abovementioned parameters representative of the global structural response.
Cdswin 2014 crack
With regard to the materials properties, Table 1 summarizes the values adopted for the masonry types that characterize the building. The values are compatible with the reference range of variation proposed in the Instructions of the Italian Technical Standards (MIT 2019) for the corresponding analogous masonry types; the reliability of these values is confirmed also by other experimental literature data (e.g. Krzan et al. 2015; Vanin et al. 2017). Consistently with what usually recommended by Codes (e.g.: NTC (2018), EC8-3 (CEN 2005)), in order to reproduce the effects of progressing cracking, a reduction factor conventionally equal to 0.50 has been applied to the gross stiffness of each element. In this respect, it is noted that the values of the elastic moduli of masonry summarized in Table 1 refer to the initial elastic condition.
As it clearly results, the main difference between the four criteria is found in the external piers, whereas in almost all the cases, the inner elements are characterized by effective heights that follow the aligned openings; only for the criterion by Dolce (1991) the resulting height for the internal piers is a bit higher. The comparison with the actual damage of these elements shows how the cracks (both in the case of diagonal cracking and of flexural failure) spread typically in a height equal to that of the adjacent openings. In the case of the external piers, the criteria proposed by Moon et al. (2006) and Augenti (2006), which are mostly based on considerations related to the development of an equivalent strut in the considered direction of analysis, seem to alternatively well capture the cracks at the upper or lower end of the elements. The adoption of such criteria requires alternative models for monotonous analysis in X and Y directions, with a significant increase in the computational effort. The criteria proposed by Lagomarsino et al. (2013) and Dolce (1991) appear therefore a reasonable compromise which, however, allow a very good match with the actual damage, considering also the cyclical nature of the seismic action and the simplification intrinsically made by EF models of neglecting the nonlinearity of node regions. Between these two criteria, that of Lagomarsino et al. (2013) finds greater agreement for external piers and this is the reason why the analyses discussed in Sect. 3 adopt this choice in a unified way across the SWs. Moreover, in Sects. 4.3 and 5.2 the effects resulting from the adoption of alternative criteria are discussed in terms of pushover curves and safety verification.
In the following, the comparison of the dynamic parameters estimated by the SWs through the execution of the modal analysis is presented. Conventionally, the modal analysis was carried out by adopting the cracked stiffness values (i.e. the same values then adopted in the non-linear static analyses).
Piers. Starting again from wall W1 (Fig. 9), almost all of the SWs estimate a prevailing flexural damage in case BS5/A, more localized in the piers at the ground floor (indeed, most SWs predict an elastic response for the piers at the first floor). For some inner piers (i.e. P08 and P09, see Fig. 9 for the elements numbering), in case of BS5/C, the majority of the SWs predict a prevailing diagonal shear cracking, while only two SWs predict a flexural response. This discrepancy can be ascribable to the range of the axial load acting on the panels, which corresponds to the region of the strength domains in which the predictions of two failure modes are very close. Thus, small differences in the variation of the axial load on the elements can lead to differences in the failure mode predicted, as also discussed in detail in Manzini et al. (2021). Apart from this aspect, also in case BS5/C an overall consistency among the SWs in predicting the concentration of the damage at the ground floor can be observed. As regards walls W3 and W9 (Fig. 11), case BS5/A shows more scattered predictions, with a clear tendency, in the transition to BS5/C, to pass to a prevalence of diagonal cracking shear failure of the piers at the ground floor. The fact that the trend in this transition from BS5/A to BS5/C is less marked for wall W1 is justified by the geometry of the piers of this particular wall, which are much slenderer than those of the other ones, and for which (all other factors being equal) a greater propensity to a flexural failure is therefore reasonable.
Spandrels. Starting from walls W6 and W8 (characterized by a more significant number of spandrels and therefore more representative), almost all of the SWs estimate the flexure plasticization (or collapse) for case BS5/A, passing in most cases to the diagonal cracking shear failure mode or to the elastic phase in case BS5/C (Figs. 12, 13 and 14). The general behavior is therefore the same observed in the X direction.
In general, a good agreement can be observed (see respectively Figs. 4 and 14 for W8, Figs. 3 and 15 for W10 and Figs. 5 and 13 for W6). In fact, as previously highlighted, in case BS5/C the SWs predict for the piers an overall response in general characterized by a more severe concentration of damage at the ground floor, with a prevalence of the diagonal cracking shear damage and with the flexural response limited to some elements at the first floor, whereas for the spandrels a shear response due to diagonal cracking or an elastic condition are predicted.
Concerning W6, the SWs are almost unanimous in predicting a diagonal cracking failure mode for the internal piers at the ground floor and a prevailing flexural damage mode for all the other piers. In the case of spandrels, the SWs estimate an almost elastic response at the top level, in agreement with the elements not damaged in reality, while they overestimated the damage of the spandrels at the intermediate level.
Concerning W10, first of all it is useful highlighting that it is characterized at each floor level by a very squat pier (responsible for balancing most of the external seismic forces) coupled to a very slender one. In most cases (4 over 6) the SWs predicted a diagonal cracking shear failure mode for the squat element, while they are unanimous in estimating a flexural failure mode for the slender one. Moreover, further in agreement with the actual damage, a concentration of the damage at the ground floor is observed. 2ff7e9595c
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